Four identical coins are placed in a square. For each coins, the ratio of area to circumference is the same as the ratio of circumference to area

Question

Four identical coins are placed in a square. For each coin, the ratio of area to circumference is the same as the ratio of circumference to the area. Then, find the area of the square that is not covered by the coins.

(a) 16(π – 1) 

(b) 16(8 – π) 

(c) 16(4 – π) 

(d) 16(4– π/2)

Answer 1

Answer : (c) 16(4 – π) 

Let ‘r’ be the radius of each circle. Then,

\(\frac{\pi r^2}{2\pi r}\) = \(\frac{2\pi r}{\pi r^2}\) ⇒ πr² = 2πr 

⇒ r = 2 (∵ r ≠ 0)

∴ Length of side of square = 4r = 8 

∴ Area of square not covered by coins 

= Area of square – Area of 4 circles

= 64 – 4π (2)² 

= 16(4 – π).